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On n × m-valued Łukasiewicz-Moisil algebras

100%
Sanza C.
Open Mathematics
|
2008
|
tom 6
|
nr 3
372-383
EN
n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM n×m -algebra is computed.
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A Topological Approach to Tense LMn×m-Algebras

100%
Figallo A. V., Pascual I., Pelaitay G.
Bulletin of the Section of Logic
|
2020
|
tom 49
|
nr 1
EN
In 2015, tense n × m-valued Lukasiewicz–Moisil algebras (or tense LMn×m-algebras) were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense LMn×m-algebras.
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Remarks on affine complete distributive lattices

88%
Zypen D.
Open Mathematics
|
2006
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tom 4
|
nr 3
525-530
EN
We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.
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